WASHINGTON — In the days after Barack Obama ordered the successful mission to kill Osama bin Laden, the president’s approval rating on foreign policy issues reached an all-time high, even as public opinion regarding his handling of the economy sunk to the lowest point of his administration, according to a new NBC News poll.

The survey shows a mixed picture for Obama, whose overall job-approval rating was bumped higher by a modest three points after the al-Qaida leader’s death was announced late Sunday.

What has changed for the president since the raid at bin Laden’s compound: The number of respondents seeing Obama as a strong leader and a good commander in chief has spiked, and public opion for his handling of the war in Afghanistan jumped to an all-time high.

But here’s what hasn’t changed: Just a third of Americans believe the country is headed in the right direction; less than four in 10 approve of Obama’s handling of the U.S. economy; and nearly 70 percent think the economy will get worse or stay the same in the next year.

“This is a poll that should both fortify the president and frighten the president as he looks ahead to re-election,” said Democratic pollster Peter D. Hart, who conducted this survey with Republican pollster Bill McInturff.

Obama’s overall job-approval rating stands at 52 percent, a three-point increase from an NBC News/Wall Street Journal poll released a month ago. Forty-one percent say they disapprove of the president’s job, representing a drop of four points.

Looking ahead to next year’s presidential election, 45 percent said they would probably vote for Obama (a two-point rise from April), versus 30 percent who would probably vote for the eventual Republican nominee (an eight-point decrease).

The survey — which was conducted May 5-7 among 800 adults (100 reached by cell phone), and which has a margin of error of plus-minus 3.5 percentage points — comes amid good and bad economic news.

The good: The U.S. economy added 268,000 private-sector jobs in April, the most since 2006. The bad: Average gasoline prices have reached nearly $4 per gallon, and the unemployment rate increased from 8.8 percent to 9.0 percent.

The president’s national-security bump
Where Obama did see a significant jump in his poll numbers were on questions about leadership, national security and foreign affairs.

According to the survey, 53 percent give the president high marks for his ability to handle a crisis (versus 44 percent last December), an equal 53 percent give him high marks for being firm and decisive (versus 41 percent last December), and 51 percent give him high marks for being a good commander in chief (versus 41 percent).

Hart, the Democratic pollster, explains that these stronger leadership numbers for Obama could become “a possible defining and tipping point” for an administration that wasn’t previously viewed this way.

It isn’t time to withdraw from Afghanistan
Yet the American public sends this overwhelming message when it comes to Afghanistan: Now is not the time to withdraw U.S. troops after bin Laden’s death in nearby Pakistan.

A whopping 72 percent agree with the statement that the United States should keep troops in Afghanistan because bin Laden’s death doesn’t change the overall mission, and because the Taliban and al-Qaida still remain threats.

By comparison, just 20 percent agree with the statement that the United States should remove troops from Afghanistan because bin Laden’s death suggests that the Taliban and al-Qaida are now less of a danger to American interests and U.S. military presence is no longer necessary in that country.

Asked another way, 52 percent approve of President Obama’s call for U.S. troops to stay in Afghanistan until 2014 — though he has said they’ll begin coming home this summer — while 46 percent disapprove.

Respondents to the poll also appeared to have a slight uptick in their level of confidence that the war in Afghanistan will come to a successful conclusion. About 38 percent say they are more confident about the outcome of the conflict (up seven percent from April), while 50 percent still say they are less confident (down 10 points from April.)

Expecting future terrorist attacks
While the public may be more optimistic about the president’s leadership on foreign policy and the war, they are still bracing for potential terrorist attacks on American soil.

A combined 52 percent say they are “very worried” or “fairly worried” about another major terrorist attack in the United States. Also, a combined 78 percent say the country is “very likely” or “somewhat likely” to be a target of a major terrorist attack at home or overseas.

And 39 percent believe bin Laden’s death will make it easier to win the global war on terrorism, compared with 38 percent who say it won’t affect it and another 15 percent who think it will make it harder.

Video: NBC poll: 80 percent say killing bin Laden was right

>>>we're debuting a new nbc news poll on this broadcast tonight, and it shows an overwhelming majority of americans support the decision to kill, not capture,
osama bin laden
. there's also news about the president, jobs, the economy. with us from washington is our political director, chief white house correspondent
chuck todd
. good evening.

>> reporter: good evening. in moments like last week, presidents do acquire
political capital
. it's no different for obama, but he didn't acquire a lot. here is his ajob approval. 52%. he was at 49% last month. he got a big spike among americans with his
approval rating
on
foreign policy
, 57%, all-time high in the poll, but look at the numbers on the handling of the economy. just 37% approve of that. 58% disapprove. you talk to many analysts in both parties and they say there are two reasons for that,
gas price
s they're high, and it's having a drag on the president. the president got a bump on the character attributes. over 50% say he has strong leadership qualities, he's got the ability to handle a crisis, he's firm and decisive, all the things a president wants going into election, but he's under that in achieving his goals, uniting the country, or sharing his views on the issue. only 20% agree with the statement that it's time to pull all troops out now, that the killing of
bin laden
means the threat is gone. 72% agree with the president's position that says, yes,
bin laden
is dead, but the threat has not gone away and troops may have to stay in afghanistan. and finally, there's a big loser in the poll, the government of pakistan. 72% do not believe the government there. they believe somehow the government knew
bin laden
was in their country.

>>speak of our election year. we're going to do a special on where all the republican candidates stand.

>>newt gingrich
is going to run for president. he let it leak that he's going to announce it on stwiter and facebook on wednesday. he had been testing the waters, but he's probably the most well known person in the race. we'll see. he's going to have a rough row to go as we tested in our own poll.